# How do you find the derivative of #y=arcsin(x^4)#?

##### 1 Answer

Dec 13, 2016

#### Explanation:

When tackling the derivative of inverse trig functions. I prefer to rearrange and use Implicit differentiation as I always get the inverse derivatives muddled up, and this way I do not need to remember the inverse derivatives. If you can remember the inverse derivatives then you can use the chain rule.

Differentiate Implicitly:

# cosydy/dx = 4x^3 # ..... [1]

Using the

# sin^2y+cos^2y -= csc^2y #

# :. (x^4)^2+cos^2y=1 #

# :. cos^2y=1-x^8 #

# :. cosy=sqrt(1-x^8) #

Substituting into [1]